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A001577 An operational recurrence.
(Formerly M1718 N0681)
0

%I M1718 N0681 #18 Sep 04 2023 23:33:10

%S 1,1,2,6,60,2880,2246400,135862272000,10376834265907200000,

%T 77540115374348238323712000000000,

%U 71611262431705169979126571320506685849600000000000000,799595359352229378487949660335170674324575940302246074414582988800000000000000000000000

%N An operational recurrence.

%C Considers recurrences u(n+1) = (d/dx) u_n(x)*u_{n-1}(x) and u(n+1) = x*(d/dx) u_n(x)*u_{n-1}(x). In latter, take u_0=1, u_1=x; setting x=1 gives sequence shown here.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H H. W. Gould, <a href="http://www.fq.math.ca/Scanned/1-1/gould.pdf">Operational recurrences involving Fibonacci numbers</a>, Fib. Quart., 1 (No. 1, 1963), 30-33.

%F Product F_k^F_{n+1-k}, k=1..n, F = Fibonacci numbers.

%t Table[Product[Fibonacci[k]^Fibonacci[n+1-k],{k,n}],{n,12}] (* _Harvey P. Dale_, May 16 2012 *)

%K nice,easy,nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Harvey P. Dale_, May 16 2012

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)